# Homework Help: An Osculating Circle HELPPP plZZ

1. Nov 24, 2007

### dmonlama

An Osculating Circle!! HELPPP plZZ urgent

1. The problem statement, all variables and given/known data
find the values of h,k and a that make the circle (x-h)^2+(y-k)^2=a^2 tangent to the parabola y=x^2+1 at the point (1,2) annd that also make the second derivatives d^2y/dx^2 have the same value on both courves.

2. Nov 25, 2007

### HallsofIvy

What have YOU done? You need to find three values, h, k, and a, and you have three pieces of information: the circle passes through (1, 2):$(1-h)^2+ (2-k)^2= a^2$; The derivative of $(x-h)^2+ (y-k)^2= a^2$ at (1, 2) is the same as the derivative of $y= x^2+ 1$ at (1, 2); the second derivative of $(x-h)^2+ (y-k)^2= a^2$ at (1, 2) is the same as the second derivative of $y= x^2+1$ at (1, 2). The first and second derivatives of $y= x^2+ 1$ at (1,2) are easy. I would recommend using "implicit differentiation" to find the derivatives of $(x-h)^2+ (y-k)^2= a^2$.

Last edited by a moderator: Nov 25, 2007